Ann increased the quantities of all the ingredients in a recipe by $60\%$. She used $80$ grams $(\text{g})$ of cheese. How much cheese did the recipe require?
Explanation: Ann used $60\%$ more cheese than the recipe required. So she used all $100\%$ that the recipe asked for plus $60\%$ more. Ann used $100\%+60\%=160\%$ of the cheese the recipe required. Percent means per hundred, so ${160\%}$ is equivalent to ${\dfrac{160}{100}}$ which is also equal to ${160\div 100}$. ${160\div 100 = 1.6}$ To find the amount of cheese in the original recipe, we need to answer, ${80\,\text{g}}$ is ${160\%}$ of what amount? We can rewrite that question as an equation. $\begin{array}{ccccc} {80\,\text{g}}&\text{is}&{160\%}&\text{of}&\text{what amount}\\\\ {80}&=&{1.6}&\times&? \end{array}$ Let's solve for the unknown amount. $\begin{aligned} \dfrac{{80}}{1.6}&=\dfrac{{1.6}\times?}{1.6}\\\\ 50&=? \end{aligned}$ The recipe required $50\,\text{g}$ of cheese.